This thesis reports an analytical solution for circular plates of linearly variable thickness, with a central circular hole, under self-weight. The plate is oriented in a horizontal position. The thickness decreases linearly with the distance from the center of the plate. Two cases are considered: Case I has the inner edge simply supported and the outer edge free; Case II has the inner edge rigidly supported and the outer edge free. The differential equation for both cases is solved in closed form for slope. Equations for radial and tangential moments are obtained directly from the slope equation. Deflections are calculated from slopes by numerical integration using Simpson's 1/3 rule. Numerical results for practical problems may be obtained either by use of a computer program which is presented or by use of tables of dimensionless coefficients. Use of computer program and tables is explained by an example.